In various embodiments, the temperature difference ΔT across a heat exchanger directly equates to a loss in exergy. The Carnot coefficients of performance for heat pumps in cooling and heating systems are:
                                                                        COP                cooling                            =                            ⁢                                                                    T                    c                                    -                                      Δ                    ⁢                                                                                  ⁢                    T                                                                                        (                                                                  T                        h                                            +                                              Δ                        ⁢                                                                                                  ⁢                        T                                                              )                                    -                                      (                                                                  T                        c                                            -                                              Δ                        ⁢                                                                                                  ⁢                        T                                                              )                                                                                                                                          COP                heating                            =                            ⁢                                                                    T                    h                                    +                                      Δ                    ⁢                                                                                  ⁢                    T                                                                                        (                                                                  T                        h                                            +                                              Δ                        ⁢                                                                                                  ⁢                        T                                                              )                                    -                                      (                                                                  T                        c                                            -                                              Δ                        ⁢                                                                                                  ⁢                        T                                                              )                                                                                                          (        1        )            
where Th and Tc are hot and cold temperatures at either end of the system and ΔT is the additional temperature difference required to transfer heat to the air through a heat exchanger. However, ΔT is constrained by the need to exchange heat at a sufficient rate; this heat flux from one fluid, through a wall, into a second fluid is a function of the combined heat transfer due to convection in both fluids and conduction and is given by
                                                        Q              =                                                                    h                    1                                    ⁢                  A                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                                      T                    1                                    ⁢                                                                          ⁢                  Q                                =                                                      h                    2                                    ⁢                  A                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                                      T                                                                                                              ⁢                      2                                                                                                                                              Q              =                                                                                          kA                      ⁢                                                                                          ⁢                      Δ                      ⁢                                                                                          ⁢                                              T                        3                                                              t                                    ⟹                                                                          ⁢                  Q                                =                                                      A                    ⁢                                                                                  ⁢                    Δ                    ⁢                                                                                  ⁢                    T                                                                              1                                              h                        1                                                              +                                          1                                              h                        2                                                              +                                          t                      k                                                                                                                              (        3        )            
where A is the surface area of the heat exchanger, t is the wall thickness, k is the thermal conductivity of the material, h1 and h2 are the heat transfer coefficients of either fluid, and Q is the heat transfer.
Power plants and other implementations are similarly limited by heat exchanger ΔT via the Carnot efficiency
                    η        =                                            T              h                        -                          (                                                T                  c                                +                                  Δ                  ⁢                                                                          ⁢                  T                                            )                                            T            h                                              (        3        )            
In various embodiments, laminar flow heat transfer and flow losses are approximated by
                    Q        =                                                            NukAΔ                ⁢                                                                  ⁢                T                            d                        ⁢                                                  ⁢                          P              fan                                =                                    8              ⁢              Aµ              ⁢                                                          ⁢                              v                2                                      d                                              (        4        )            
where Nu is the Nusselt number, d is the effective tube diameter, Pfan is the required fan power, μ is the viscosity, and v is the fluid velocity.
The heat transfer rate in a heat exchanger can be directly proportional to the surface area in the heat exchanger. Increasing the surface area can increase the overall heat transfer, thereby increasing performance. This can be impractical with conventional heavy metallic heat exchangers. Additionally, conventional metallic heat exchangers become fragile and corrosion sensitive at small thickness.
Metallic fin-and-tube heat exchangers, similar to automotive radiators, are the current standard for conventional heat exchangers. Most metals have high densities and become fragile and corrosion sensitive at thin film thicknesses. Thus, metallic heat exchangers are heavier and more expensive than otherwise required for a given operating pressure or desired heat transfer rate, and typically rely on high-power fans which reduce efficiency.
In view of the foregoing, a need exists for improved membrane heat exchanger systems and methods in an effort to overcome the aforementioned obstacles and deficiencies of conventional systems.
It should be noted that the figures are not drawn to scale and that elements of similar structures or functions are generally represented by like reference numerals for illustrative purposes throughout the figures. It also should be noted that the figures are only intended to facilitate the description of the preferred embodiments. The figures do not illustrate every aspect of the described embodiments and do not limit the scope of the present disclosure.